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#1943
Girl Power
Participant

Just realized, that if I choose to reroll all 5 dice, I still have the possibility of achieving both five sixes and combinations of only ones and fives OR only twos and fours. So, the problem should be stated like this:
Is the probability of getting [6] [6] with TWO dice in two rolls higher than the sum of the probabilities of achieving the following combinations with FIVE dice in two rolls?
[6] [6] [6] [6] [6]
[5] [5] [5] [5] [1]
[5] [5] [5] [1] [1]
[5] [5] [1] [1] [1]
[5] [1] [1] [1] [1]
[4] [4] [4] [4] [2]
[4] [4] [4] [2] [2]
[4] [4] [2] [2] [2]
[4] [2] [2] [2] [2]
[3] [3] [3] [2] [1]
[3] [3] [2] [2] [1]
[3] [3] [2] [1] [1]
[3] [2] [2] [2] [1]
[3] [2] [2] [1] [1]
[3] [2] [1] [1] [1]
Is this difficult to calculate? (I don’t know much about probability theory)